Project Summary In chronic diseases research, understanding and accounting for individual differences caused by genetic, environmental, and lifestyle factors have become increasingly important for successful disease management. Dynamic regression, as shown by recent work including ours, is a powerful technique to characterize and identify inhomogeneous associations that explain individual variability of disease progression. The overall ob- jective of this grant is to advance dynamic regression methodology to better meet the critical need of uncovering disease mechanism heterogeneity with improved capacity to handle longitudinal/survival outcomes and covariates in various complex forms (e.g. time-varying, high-dimensional, constrained). This application is motivated by our ongoing collaborations on Feeding Infants Right.. from the STart (FIRST) study. Under the overreaching goal to identify optimal care for infants with Cystic Fibrosis (CF), FIRST has systematically captured data on complete feeding history and longitudinally collected biomarkers (e.g. blood lipids and fecal microbiota) and accessed nutritional status and pulmonary disease throughout infancy. With the rich data collection, FIRST provides an unprecedented opportunity to exploit new sensible quanti?cations of early CF phenotype (e.g. pulmonary, growth) and their dynamic associations with observed factors (e.g. genotype, environmental factors); to assess breast/formula feeding schemes for CF infants; to ?ll in the information gap on the in?uence of biomarkers on growth and their relationships to feeding. The speci?c aims of this grant are to develop innovative and effective dynamic regression tools that can help achieve these impactful scienti?c goals: (1) We will investigate a sensible modeling perspective that focuses on subject-level latent characteristics (called latent individual risk feature (LIRF) hereafter) as a substantive re?ection of disease risk/status (e.g. length growth rate ). We will develop formal dynamic regression methods for delineating the heterogeneity in LIRF, which are not available in literature (Aim1). (2) We will develop an innovative survival dynamic regression strategy that enables a comprehensive assessment of the overall impact of time-dependent exposures (e.g. feeding history) on survival outcomes (e.g. time to pulmonary exacerbation). Current methods usually describe the effects of time-dependent covariates progressively over time and thus have limited utility for evaluating different feeding schemes (Aim2). (3) We will develop new dynamic regression approaches that give an integrative account of important data challenges/features (e.g. high-dimensionality, constraints, longitudinal outcomes, time-dependent covariates) for properly assessing the mechanisms/roles of biomarkers during CF infancy (Aim3). (4) The proposed statistical methods will be applied to FIRST and user-friendly software will be developed (Aims 4-5). Although speci?cally motivated by CF studies, the proposed methodologies are generally applicable to many other chronic diseases.